From 8.30 pm to 12 : 00
Difference = 12 : 00 - 08:30 = 3 : 30
3 hours 30 minutes = 3.5 hours.
Total for those hours = 3.5 * 1000 = $3500
From 12:00 to 1:00 am = 1 hour.
50% increase = 50% of 1000 = .50 * 1000 = 500
So it will increase to 1000 + 500 = $1500 per hour.
For the 1 hour extra, 1 * 1500 = $1500
Total = $3500 + $1500 = $5000
She will be paid $5000
Answer:
the dimensions that minimize the cost of the cylinder are R= 3.85 cm and L=12.88 cm
Step-by-step explanation:
since the volume of a cylinder is
V= π*R²*L → L =V/ (π*R²)
the cost function is
Cost = cost of side material * side area + cost of top and bottom material * top and bottom area
C = a* 2*π*R*L + b* 2*π*R²
replacing the value of L
C = a* 2*π*R* V/ (π*R²) + b* 2*π*R² = a* 2*V/R + b* 2*π*R²
then the optimal radius for minimum cost can be found when the derivative of the cost with respect to the radius equals 0 , then
dC/dR = -2*a*V/R² + 4*π*b*R = 0
4*π*b*R = 2*a*V/R²
R³ = a*V/(2*π*b)
R= ∛( a*V/(2*π*b))
replacing values
R= ∛( a*V/(2*π*b)) = ∛(0.03$/cm² * 600 cm³ /(2*π* 0.05$/cm²) )= 3.85 cm
then
L =V/ (π*R²) = 600 cm³/(π*(3.85 cm)²) = 12.88 cm
therefore the dimensions that minimize the cost of the cylinder are R= 3.85 cm and L=12.88 cm
(a) y = 2x + 3
(b) (1,5), (3,3); y = 3x + 3 5 = m1 + b, 3 = m3 + b
(c) coincident i believe, because it is not independent or inconsistent
(d) 2x + 3 = 3x + 3
(-2x)(-3) (-2x)(- 3)
0 = -2x
x = 0
hope this helps
Answer:
86
Step-by-step explanation:
Answer:
-2/9
Step-by-step explanation:
